performance of space time block codes and quasi orthogonal space time...

Performance of Space Time Block Codes and Quasi Orthogonal Space Time Codes on

Fading Channel

Sajjad Ahmed Ghauri1, Bilal Arshad

1, Agha Saif

1, I. M. Qureshi

2

1National University of Modern Languages, Islamabad, Pakistan

2Air University, Islamabad, Pakistan

Abstract

In this paper the performance of Space Time

Codes (STC) & Quasi Orthogonal Space Time Block

Codes (QOSTBC) has been analyzed. Use of multiple

antennas is an emerging approach for recovering

fading and reducing the bit error rate. Space

diversity is introduced in space time codes. In

Alamouti Space Time Code (STC) two transmit

antennas are used that provide relatively better

results than no coding approach. Alamouti uses a

code matrix at transmitter and at receiver end it uses

MLD and estimates the output signals. Space time

block codes are with arbitrary number of antennas. It

uses a huge code matrix at encoder and decodes

using MLD. QOSTBC is one of the latest variants of

the STBCs. The encoded symbols are mapped in the

transmission matrix which is decoded at the receiver

end using pair wise maximum likelihood decoding

(MLD). Pair wise MLD is the specialty of the

QOSTBC. The performance of STBC is far better

than Alamouti and has no match with no coding. The

performance comparison of QOSTBC, Alamouti,

STBC and no coding is showed using simulations in

MATLAB. Space time codes works with the price of

redundancy bits and extra antenna price. Simulation

results for QOSTBC also shows better performance

with the price of slightly increased decoding

complexity.

1. Introduction

Mobility, accessibility and probability are the

factors that make a wireless system more attractive to

the end user. Today the world is merging into

wireless technology and despite of the fact that wired

system is more reliable, more stable and have a better

performance, the user are trying to get into the

regime of wireless technology.

Fading leads to attenuation of the signal. The

fading causes the system to be limited to a certain bit

rate and quality of service. There is more chance of a

high error performance which is not attractive to end

user. The fading in the channel is caused due to

certain factors present in the free air those factors

might be temperature, scattering, diffraction,

attenuation or non LOS communication.

One of the major drawbacks of these wireless

systems is the limited bandwidth available to them.

This of course does not concern the user but is indeed

a big issue. Having a limited bandwidth means that

only a limited number of users can be entertained in

the available spectrum.

In order to increase the capacity of the wireless

systems for providing high bit-rates to the users, new

techniques have been developed over the years. One

of the techniques is using space time block codes.

And its variant QOSTBC is a type of non-orthogonal

space time block codes and gives better performance

when the system is composed of more than two

antennas.

2. System Model

(a) Alamouti STC

One of the first and basic STCs is Alamouti Space

Time Code (ASTC) that provides transmits diversity.

Using 2 transmit antennas instead of one is the main

theme behind the space time codes. Inserting the

transmit diversity decreases the error rate

considerably.

At the receiver end one and two antennas are

used. An information source is taken that may be a

stream of bits or a voice. BPSK modulation is done.

The encoder takes an input of 2 symbols from the

modulated output. The encoder has an Alamouti

matrix that maps those bits according to following

matrix X:

(1)

In first time slot x1 and x2 will be sent and on 2nd

time slot x2* and x1

* would be transmitted. The

transmitted signals pass through Rayleigh fading

channel. Rayleigh faded noise is been added to them

in that channel. The received signals are represented

International Journal for Infonomics (IJI), Special Issue Volume 1, Issue 1, 2013

Copyright © 2013, Infonomics Society 797

by r1 and r2. The following equation shows the

received signals at the receiver.

(2)

where

nT= Number of transmit antennas

ri= Received bits from ith transmit antenna

ai= The path gain matrix

xi= The bits at the ith

transmit antenna

ni= Rayleigh faded noise for ith

antenna

At the receiver end maximum likelihood

decoding is used. We can implement MLD linearly in

ASTC decoder. MLD forms decision variables and

estimates the received signal ri. Following is the

formulae for the decision variables

(3)

Ri = decision variable

rt = Received signal of the tth

transmit antenna.

t = Sign of the transmitted bit

After finding the decision variables through MLD the

receiver estimates from the constellation that satisfies

the following equation.

(4)

(b) Space Time Block Codes

As discussed in ASTC that provided diversity for

two transmit and one, two receive antenna. Alamouti

scheme was proposed for two transmit antennas, to

increase the range of transmit antennas to an arbitrary

number Space Time Block Codes STBC were

introduced. STBC is actually a generalized form of

ASTC in which we can increase the transmit

antennas keeping in touch with the spatiality of

ASTC of orthogonality between the transmitted

signals on respected antennas. In this section STBC

will be discussed and we will also focus on factors

like code rate because with increase in antennas there

comes complexity in the code matrix and we might

have to sacrifice some bandwidth for it. At the

encoder side information bits are produced and

modulated using BPSK modulation scheme. The

code matrix for the encoder of STBC is a bit

complex. For real signals the code matrix X shown

below is for 4 transmit antennas, it will be different

for other numbers of antennas.

(5)

where the code rate is R=k/p, k is number of bits

taken by the encoder and p is number of bits

transmitted through each antenna in a single time

slot. The code matrix X for real signals the code rate

is 1. Code rate of 1 means that there would be no

need for increasing the bandwidth. If the code rate is

less than 1 then the bandwidth would have to be

expanded by the factor 1/R. The encoder takes k=4

real modulated symbols x1, x2, x3, x4 as its input.

Then these symbols are passed through the code

matrix and they are mapped all over it. Then output is

a 4x4 matrix. The matrix is then mounted on each

antenna row by row and those rows are then

transmitted. In first time slot x1, x2, x3, x4 are

transmitted from Tx1. The transmitted signals pass

through Rayleigh fading channel. The received

signals are represented by r1 and r2. At the receiver

end maximum likelihood decoding is used. We can

implement MLD linearly in STBC decoder. MLD

forms decision variables and estimates the received

signal ri.

(c) Quasi Orthogonal Space Time Block Codes

QOSTBC is a type of non-orthogonal STBC. Its

transmission matrix is not entirely non orthogonal but

is partially orthogonal. It is more suitable when using

more than two antennas at the transmitter side in the

wireless system. QOSTBC provide full diversity, rate

one and simple pair wise decoding can be performed

and relatively better results are achieved. Four

transmit antennas and one receive antenna are used.

The information source provides the bits to be

transmitted. Two types of modulation are used:

QPSK and rotated QPSK. In rotated QPSK, the

symbols are rotated and form a rotated constellation.

Rotated QPSK provide full diversity in QOSTBC.

The symbols to be transmitted are fed to the encoder

which than maps them in the following general

matrix X

X=

(6)

We have four transmit antennas and each antenna

will transmit one element from a row in one timeslot

hence one row of symbols will be transmitted in one

timeslot. So in the first timeslot, x1, x2, x3 and x4 will

be transmitted and vice versa. Let the symbols to be



transmitted are s1, s2, s3 and s4. The symbols which

rotate are s3 and s4 to get full diversity. Then the

rotated symbols in radians are

and . The other two symbols s1 and s2 will

be transmitted without rotation. These transmitted

symbols passed through a Rayleigh fading channel

after passing through the Rayleigh fading channel,

the faded symbols are received at the receiver

antenna. For QOSTBC, we use pair wise maximum

likelihood decoding. We can decode a pair of

symbols independently in QOSTBC. We can decode

the received symbols using the following equations:

For s1 and s4

For s2 and s3,

where s1 & s2= transmitted symbol and α are path

matrix and r is symbol matrix.

3. Simulation Results

The implementation of ASTC for two transmit,

one receive and two transmit, two receive antenna

has been done.

(a)

(b)

Figure 1: (a) Performance Comparison of Alamouti

with one and two receive antennas with 2 transmit

antennas, (b) Comparison of Alamouti with

transmission without coding.

(7)

(8)



(a)

(b)

Figure 2: (a) STBC with 2 and 4 receive antennas and

4 transmit antennas. (b) Comparison of STBC with

transmission without coding.

Figure 3: Simulation Result for Alamouti, STBC and

no coding.

The simulation result of Figure 4 shows the

performance comparison of QOSTBC with no coding

and BER performance is much better with low SNR.

Figure 4: QOSTBC with 1 receive antennas and 4

transmit antennas compared with no coding on

Rayleigh fading channel

Figure 5: QOSTBC with 1 receive antennas and 4

transmit antennas compared with no coding and

STBC with 4 and 2 transmit and receive antennas on

Rayleigh fading channel.

The performance comparison of QOSTBC and

STBC on Rayleigh fading channel is shown in Figure

5. The simulation shows that QOSTBC performs

better at low SNR but high complexity.

4. Conclusion

The simulation result illustrate that out of

Alamouti and STBC, STBC are worth to be

implemented on the wireless communication

systems. As they are providing far less bit error rate

as compare to no coding communication. Increase in



the number of transmit and receive antennas

enhances the performance of STBC.

The simulation Figure 3 shows the comparison of

Alamouti, STBC and no coding. STBC with 4

transmit and 4 receive antennas has the best result of

all. So we can say that if we increase the number of

antennas the result would be better but the tradeoff in

such approach is the increase in the computations at

the receiver end.

The QOSTBC can provide full code rate and full

diversity. Its decoding complexity is a little higher

than the orthogonal STBCs but is still less than that

of the non-orthogonal STBCs. QOSTBC outperforms

(in a bit-error rate sense) the fully orthogonal 4-

antenna STBC over a good range of signal-to-noise

ratios (SNRs). It performs better at higher SNRs and

better than STBC.

5. References

[1]B. Vucetic, J. Yuan, ”Space-Time Coding”, John Wiley

& Sons, England, 2003.

[2] Z. Liu, G. B. Giannakis, S. Zhou, B. Muquet, ”Space-

time coding for boradband wireless communications”,

Wireless Communications and Moblie Computing, vol. 1,

no. 1. pp. 35-53, Jan. 2001.

[3]Sajjad Ahmed Ghauri, M. Sajid Javed, M. Raza Parvez

,Bilal Ahmed “Performance of Space Time Codes on

Fading Channel” IEEE conference of Information Society

UK, 2012.

[4]M. T. Ivrlac, T. P. Kurpjuhn, C. Brunner, W. Utschick,

“Efficient use of fading correlation in MIMO systems”,

54th VTC, Atlantic City, USA, vol. 4, pp. 2763-2767, Oct.

2001.

[5] J. G. Proakis, Digital Communications, 4th Ed.,

McGraw-Hill, New York, 2001.

[6]Sajjad Ahmed Ghauri, M. Ehsan ul Haq, Farhan Sohail,

Bilal Ahmad “Performance of Space Time Trellis Code on

Fading Channel” 8th IEEE conference on Wireless &

Mobile computing, Networking & communication, Spain,

2012.

[7]S. M. Alamouti, “A simple transmit diversity technique

for wireless communications”, IEEE Journal Select. Areas

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[8]A. Naguib, V. Tarokh, N. Seshadri and A.Calderband,

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[9]S. M. Alamouti,”A simple transmit diversity technique

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[11]J. Grimm, M.P.Fitz andJ.V.Krogmeier, “Further

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[12]A.R.Hammons and H.E. Gammal,“On the theory of

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[13]S. Baro, G. Bauch and A. Hansmann, “Improved Codes

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[14]Q. Yan and R.S.Blum, “Optimum space-time

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[15]Z. Chen, J.Yuan and B.Vucetic, “Improved space-time

trellis coded modulation scheme on slow Rayleigh Fading

channels”.

[16]Z. Chen, J.Yuan, B.Vucetic and K. Lo, “space-time

trellis coded modulation with three and four transmit

antennas on slow fading channels”.

[17]Z. Chen, J.Yuan, B.Vucetic and W.

Firmanto,”Performance analysis and design of space-time

coding on fading channel”.



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